1SSPR2(1)                         BLAS routine                         SSPR2(1)
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NAME

6       SSPR2  -  performs  the  symmetric rank 2 operation   A := alpha*x*y' +
7       alpha*y*x' + A,
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SYNOPSIS

10       SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
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12           REAL                                        ALPHA
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14           INTEGER                                     INCX,INCY,N
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16           CHARACTER                                   UPLO
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18           REAL                                        AP(*),X(*),Y(*)
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PURPOSE

21       SSPR2  performs the symmetric rank 2 operation
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23       where alpha is a scalar, x and y are n element vectors and A is an n by
24       n symmetric matrix, supplied in packed form.
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ARGUMENTS

28       UPLO   - CHARACTER*1.
29              On  entry,  UPLO specifies whether the upper or lower triangular
30              part of the matrix A is supplied in the packed array AP as  fol‐
31              lows:
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33              UPLO  =  'U' or 'u'   The upper triangular part of A is supplied
34              in AP.
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36              UPLO = 'L' or 'l'   The lower triangular part of A  is  supplied
37              in AP.
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39              Unchanged on exit.
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41       N      - INTEGER.
42              On  entry,  N specifies the order of the matrix A.  N must be at
43              least zero.  Unchanged on exit.
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45       ALPHA  - REAL            .
46              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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48       X      - REAL             array of dimension at least
49              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the  incremented
50              array X must contain the n element vector x.  Unchanged on exit.
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52       INCX   - INTEGER.
53              On  entry,  INCX  specifies the increment for the elements of X.
54              INCX must not be zero.  Unchanged on exit.
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56       Y      - REAL             array of dimension at least
57              ( 1 + ( n - 1 )*abs( INCY ) ).  Before  entry,  the  incremented
58              array Y must contain the n element vector y.  Unchanged on exit.
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60       INCY   - INTEGER.
61              On  entry,  INCY  specifies the increment for the elements of Y.
62              INCY must not be zero.  Unchanged on exit.
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64       AP     - REAL             array of DIMENSION at least
65              ( ( n*( n + 1 ) )/2 ).  Before entry with  UPLO =  'U'  or  'u',
66              the  array AP must contain the upper triangular part of the sym‐
67              metric matrix packed sequentially, column by column, so that AP(
68              1  )  contains  a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
69              and a( 2, 2 ) respectively, and so on. On exit, the array AP  is
70              overwritten  by the upper triangular part of the updated matrix.
71              Before entry with UPLO = 'L' or 'l', the array AP  must  contain
72              the lower triangular part of the symmetric matrix packed sequen‐
73              tially, column by column, so that AP( 1 ) contains a(  1,  1  ),
74              AP(  2  )  and  AP(  3 ) contain a( 2, 1 ) and a( 3, 1 ) respec‐
75              tively, and so on. On exit, the array AP is overwritten  by  the
76              lower triangular part of the updated matrix.
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FURTHER DETAILS

79       Level 2 Blas routine.
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81       -- Written on 22-October-1986.
82          Jack Dongarra, Argonne National Lab.
83          Jeremy Du Croz, Nag Central Office.
84          Sven Hammarling, Nag Central Office.
85          Richard Hanson, Sandia National Labs.
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90BLAS routine                     November 2008                        SSPR2(1)